Method and Apparatus for Accurate Calibration of VUV Reflectometer

ABSTRACT

A calibration technique is provided that utilizes a standard sample that allows for calibration in the wavelengths of interest even when the standard sample may exhibit significant reflectance variations at those wavelengths for subtle variations in the properties of the standard sample. A second sample, a reference sample may have a relatively featureless reflectance spectrum over the same spectral region and is used in combination with the calibration sample to achieve the calibration. In one embodiment the spectral region may include the VUV spectral region.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/930,339, filed Aug. 31, 2004, which claims priority to ProvisionalPatent Application No. 60/600,599 filed Aug. 11, 2004; the disclosure ofwhich is expressly incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to the field of optical metrology. Morespecifically, it provides a method by which broad-band vacuumultraviolet (VUV) reflectance data may be accurately calibrated.Additionally, it also provides a method by which highly accurate thinfilm measurements may be performed.

Optical reflectometry techniques have long been employed in processcontrol applications in the semiconductor manufacturing industry due totheir non-contact, non-destructive and generally high-throughput nature.The vast majority of these tools operate in some portion of the spectralregion spanning the deep ultraviolet and near-infrared wavelengths(DUV-NIR generally 200-1000 nm). The push towards thinner layers and theintroduction of complicated new materials have challenged thesensitivity of such instrumentation. As a result, this has necessitatedan effort to develop optical reflectometry equipment utilizing shorterwavelengths (below 200 nm), where greater sensitivity to subtle changesin material properties may be realized. One approach to performing suchmeasurements is described in U.S. application Ser. No. 10/668,642, filedon Sep. 23, 2003, which discloses a system and method for a vacuumultraviolet (VUV) reflectometer, the disclosure of which is incorporatedherein by reference.

To obtain meaningful quantitative results from reflectometry data it isdesirable to normalize or calibrate measured reflectance values in orderto generate absolute reflectance spectra. At longer wavelengths in theDUV-NIR region this has traditionally been accomplished using a varietyof techniques involving complicated optical arrangements thatincorporate moving mirrors. Examples of such methods are provided inU.S. Pat. No. 4,368,983 (and references incorporated therein) whichdescribes an apparatus and method to measure the absolute reflectivityof a sample using a multiple pass reflectometer.

While such methods offer a means of obtaining calibrated reflectancedata, they generally suffer from the fact that they are time-consuming,involve considerable mechanical motion and can not easily be integratedinto systems suitable for use in semiconductor manufacturingenvironments. Furthermore, many of these methods were designed for usein single wavelength reflectometers wherein a single wavelength detectoris used in combination with a wavelength selecting pre-monochromator.

Ideally, it would be desirable to provide a technique by whichbroad-band reflectometry data could be simultaneously calibrated quicklyand simply and in a manner that would lend itself suitable for use insemiconductor manufacturing environments.

One calibration approach is presented in U.S. Pat. No. RE 34,783 whereina method is described that involves measuring the reflectance from acalibration sample whose absolute reflectance is well known, dividingthe measured value by the absolute value to obtain a system efficiencycoefficient and then, without changing the illumination or optics,measuring the reflectance of an unknown material and applying thecoefficient to the measured value to obtain its absolute value.

In practice, single crystal silicon wafers are commonly employed ascalibration samples since they are readily available, controllablymanufactured and their optical properties in the DUV-NIR region havebeen well characterized. This approach works reasonably well atwavelengths above ˜250 nm where the reflectance of single crystalsilicon is both stable and predictable.

At shorter wavelengths (<250 nm) the reflectance of single crystalsilicon wafers is neither stable nor predictable. Subtle variations inthe thickness of the naturally (or “native”) formed silicon dioxidelayer present on the wafer can significantly influence the measuredreflectance. Additionally, ultra-thin layers of moisture and/orhydrocarbons are known to adsorb onto the surface further modifying thesample reflectance in this spectral region. As a result, it is generallynot advisable to regard the reflectance of single crystal silicon wafersat wavelengths <250 nm as a “known” property.

One approach to overcoming this problem is presented in U.S. Pat. No.5,798,837, which describes an optical measurement system that includes areference ellipsometer and at least one non-contact optical measurementdevice, such as a reflectometer. The reference ellipsometer is used todetermine an optical property of the calibration sample. The opticalmeasurement device is then calibrated by comparing the measured opticalproperty from the optical measurement device to the determined opticalproperty from the reference ellipsometer.

Integration of a separate reference ellipsometer into an opticalmeasurement system in order to calibrate the first optical measurementdevice is both complicated and expensive. Furthermore, the referenceellipsometer itself must be properly aligned and calibrated if it is toyield accurate results.

It follows that it would be highly desirable to develop a means ofquickly and accurately calibrating broad-band data from an opticalreflectometer operating at wavelengths <250 nm without the complicationand expense associated with incorporating a second reference instrumentinto the system.

Additionally, it would be advantageous if this method specificallyenabled the accurate calibration of reflectometry data at wavelengthsencompassing the VUV spectral region, where small uncertainties in theproperties of third party certified standards can result in substantialerrors. It would be further desirable if this method was capable ofindependently determining the properties of such standards so as toreduce or altogether remove the need for their procurement andmaintenance.

In addition to providing a technique to enable accurate calibration ofreflectometry tools, it is desirable to provide a technique by whichhighly accurate thin film measurements may be performed. Opticalreflectance measurements are used in a wide range of thin filmapplications. Ordinarily the absolute reflectance of a sample isrecorded and subsequently analyzed using mathematical models in order todetermine an assortment of physical properties.

Typically, the analysis is deemed complete when a quantitative indicator(generally referred to as the “goodness of fit” parameter) attains aspecific value. Unfortunately, there are limits to the measurementaccuracy that can be attained using conventional “goodness of fit”parameters. Hence, it follows that it would be desirable to develop amore sensitive measure of “goodness of fit” in order that higher levelsof accuracy in thin film measurement may be obtained.

SUMMARY OF THE INVENTION

One embodiment of the current invention provides a means by which VUVreflectance data may be quickly and accurately calibrated. In oneembodiment, the method enables simultaneous calibration of reflectancedata covering a broad range of wavelengths. Additionally, the techniqueoperates in a manner well suited for use in semiconductor manufacturingenvironments.

The method may be self-contained in that it may not require use of asecond referencing instrument. It may provide a method by whichcalibration results may be autonomously verified such that use of thirdparty certified standards will be reduced and/or altogether eliminated.

In one embodiment, the techniques include utilizing a standard (or“calibration”) sample that allows for calibration in the wavelengths ofinterest even when the standard sample may exhibit significantreflectance variations at those wavelengths for subtle variations in theproperties of the standard sample. Thus, calibration may be achievedeven in cases where traditionally significant calibration error inregions of wavelengths that a user is interested in would be expected tobe encountered. In this regard the technique takes advantage of thepresence of a certain amount of calibration error that may be referredto as a calibration error function.

In another embodiment, the calibration process may include a techniquethat utilizes a first sample and a second sample. The first sample mayinclude significant reflectance variation in the spectral region ofinterest as a function of sample property variations and the secondsample may have a relatively featureless reflectance spectrum over thesame spectral region. The first sample may be considered a standard orcalibration sample and the second sample may be considered a referencesample. In one embodiment the spectral region may include the VUVspectral region.

In another embodiment a calibration technique is provided in which astandard or calibration sample may have relatively unknown propertieswith the exception that it may be assumed to have a significantcalibration error function in the spectral regions of interest. Thus,the exact properties of the standard sample need not be known if it canbe assumed that the standard sample exhibits sharp changes inreflectance for changes in the sample property.

In another embodiment of the current invention a technique by whichhighly accurate thin film measurements may be performed is provided. Themethod may provide mathematical fitting algorithms with a more sensitive“goodness of fit” indicator that is less susceptible to noise present inthe raw data. The fitting routine may be a spectrally driven fittingroutine rather than relying solely on an amplitude driven routine (whichtypically incorporates difference calculations). In such an embodiment,the measurements may be obtained by utilizing the presence of sharp,narrow spectral features.

In one embodiment, the measurements are obtained by a spectrally drivenfitting routine that utilizes a ratio of an expected reflectancespectrum of the sample being measured to the actual reflectance spectrumof the sample being measured. Thus, rather than being based upon adifference between the expected and actual values, the techniquesprovided herein utilize a ratio of the values. The techniques areparticularly useful in spectral regions that contain sharp spectralfeatures, for example the sharp features that are often exhibited in theVUV region for thin film samples. Thus, a data convergent technique isprovided that may beneficially utilize an absorption edge effect of thematerial is disclosed. In this manner sharp spectral features, forexample resulting from either interference or absorption effects areadvantageously utilized to better determine a data minimum that isindicative of an actual measurement value.

In another embodiment, the data reduction techniques may utilize a twostep approach. In such an embodiment a low resolution step such as anamplitude driven fitting routine may be used to first provide a “coarse”measurement. Then a high resolution step such as a spectrally-drivenfitting routine that advantageously utilizes the presence of sharpspectral features may be used to provide a “fine” measurement. In oneembodiment, the low resolution step may obtain a rough measurement valueby using a difference based technique as in a “Chi-square” meritfunction. The high resolution step may be a spectrally driven step thatincludes a ratio based technique in the region of interest initiallyidentified by the low resolution technique.

A further understanding of the nature of the advantages of the presentinvention may be realized following review of the following descriptionsand associated drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates a prior art calibration and measurement flowchart fora reflectometer.

FIG. 2 illustrates a prior art detailed calibration and measurementflowchart for a reflectometer.

FIG. 3 illustrates reflectance spectra from ultra-thin SiO2/Si samples.

FIG. 4 illustrates calibration error spectra for a 20 Å SiO2/Si samplegenerated for a series of assumed thicknesses.

FIG. 5 illustrates an exemplary calibration and measurement flowchartaccording to one embodiment of the present invention.

FIG. 6 illustrates calibration error spectra for a 10000 Å SiO2/Sisample generated for a series of assumed thicknesses.

FIG. 7 illustrates a reflectance spectra for a broad-band VUV mirror(#1200) manufactured by Acton Research Corp.

FIG. 8 illustrates a product of a reference sample reflectance spectrumand a calibration error function for a 10000 Å SiO2/Si sample obtainedfrom the measurement of an arbitrary reference sample.

FIG. 9 illustrates a derivative of a calibration error function for a10000 Å SiO2/Si sample generated for an assumed thickness of 10010 Å.

FIG. 10 illustrates a sensitivity plot calculated using a calibrationerror function integral for a 10000 Å SiO2/Si standard sample.

FIG. 11 illustrates a reflectance of a reference sample used in acalibration routine.

FIG. 12 illustrates an exemplary detailed calibration and measurementflowchart according to one embodiment of the present invention.

FIG. 12A illustrates an exemplary reflectometer system which may utilizethe calibration concepts of the present invention.

FIG. 13 illustrates the sensitivity plot calculated using a standardprior art merit function for a 10000 Å SiO2/Si sample.

FIG. 14 illustrates an expanded sensitivity plot calculated using astandard prior art merit function for a 10000 Å SiO2/Si sample in thepresence of 1% noise on the measured reflectance data.

FIG. 15 illustrates an exemplary detailed measurement flowchartaccording to one embodiment of the present invention.

FIG. 16 illustrates an expanded sensitivity plot calculated using an MEFintegral for a 10000 Å SiO2/Si sample in the presence of 1% noise on themeasured reflectance data.

FIG. 17 illustrates a sensitivity plot calculated using an MEF integralfor a 10000 Å SiO2/Si sample.

FIG. 18 illustrates a comparison of sensitivity plots calculated usingan MEF integral and a standard prior art merit function for a 100 ÅSiO2/Si sample.

FIG. 19 illustrates an expanded sensitivity plot calculated using an MEFintegral for a 100 Å SiO2/Si sample in the presence of 1% noise on themeasured reflectance data.

FIG. 20 illustrates an expanded sensitivity plot calculated usingstandard prior art merit function for a 100 Å SiO2/Si sample in thepresence of 1% noise on the measured reflectance data.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The manner in which standard samples are typically used to calibratereflectometers is generally presented in the flowchart 102 of FIG. 1. Asis evident in the figure the first step 104 in the calibration processis to assume knowledge of the reflectance properties of the standardsample. With this information in hand, the intensity of light reflectedfrom the sample as a function of wavelength can be recorded and thereflectometer calibrated in step 106. Subsequently, the reflectance ofunknown samples may then be absolutely determined with the device instep 108.

A more detailed description of this calibration procedure is outlined inthe flowchart 202 of FIG. 2 wherein the mathematical relationshipsinvolved in calculating the absolute reflectance of an unknown sampleare presented. FIG. 2 illustrates the flowchart 202 for the calibrationprocedure. In a first step 204, knowledge of reflectance properties of astandard sample is assumed. Then in step 206 the intensity from thestandard sample is recorded. Next the source intensity profile iscalculated in step 208 using knowledge of the assumed reflectanceproperties of the standard sample. In step 210, the intensity from anunknown sample is recorded. The reflectance of the unknown sample maythen be calculated as shown in step 212. The reflectance of the unknownsample may then be expressed according to the equation of step 214. Fromexamination of the final step of the process it is evident that themeasured reflectance of an unknown sample is directly proportional tothe assumed reflectance of the calibration sample. Hence, if the assumedreflectance is inaccurate it follows that the measured reflectance willalso be inaccurate.

Single crystal silicon wafers have long been used as calibrationstandards for reflectometers operating in the DUV-NIR. They have proveda sensible choice as they are ubiquitous, controllably manufactured andoptically well characterized in this spectral region. In practice theassumed reflectance properties for the silicon wafer are calculatedusing the Fresnel Equations and an assumed knowledge of the opticalproperties and thickness of the native silicon dioxide surface layer andthe optical properties of the silicon itself.

When employed for the calibration of reflectometers operating atwavelengths longer than about 250 nm silicon wafers work well since theunderlying assumptions regarding their physical properties arerelatively insensitive to error in this wavelength region. In otherwords, errors in the assumed thickness of the native oxide layer on thesurface of the wafer do not significantly influence the expectedreflectance of the sample and hence negatively impact the accuracy ofthe calibration process.

This point is further illustrated in FIG. 3 wherein calculatedreflectance spectra for a series of SiO₂/Si samples with SiO₂thicknesses ranging from 10 to 30 Å are presented. For example,reflectance spectrum 302 illustrates a Si sample having a 10 Å SiO₂layer while reflectance spectrum 304 illustrates a Si sample having a 30Å SiO₂ layer. While differences between the spectra are reasonably smallabove 250 nm, they become quite significant at shorter wavelengths.Hence, if the thickness of the native oxide layer is assumed to be 10 Åand is actually 20 Å then a considerable calibration error will beintroduced at wavelengths lower than 250 nm.

FIG. 4 better illustrates the effect of such errors. Plotted in thisfigure are a series of curves corresponding to the ratios of pairs ofreflectance spectra. The first spectrum in each pair corresponds to thatexpected from a SiO₂/Si sample with an “assumed” native oxide thickness(ranging from 10 to 30 Å), while the second spectrum in each paircorresponds to a SiO₂/Si sample with an “actual” native oxide thicknessof 20 Å. Thus, curve 302 of FIG. 4 corresponds to the ratio of thereflectance spectrum for an assumed native oxide thickness of 10 Å tothe reflectance spectrum of a native oxide thickness of 20 Å. Similarlycurve 304 of FIG. 4 corresponds to the ratio of the reflectance spectrumfor an assumed native oxide thickness of 15 Å to the reflectancespectrum of a native oxide thickness of 20 Å. In a similar fashioncurves 306, 308 and 310 illustrate the ratio of an assumed native oxidethickness of 20, 25, and 30 Å (respectively) to the reflectance spectrumof a native oxide thickness of 20 Å. In this sense the ratio may beconsidered essentially as a measure of calibration error, hereinreferred to as the calibration error function (CEF). The closer CEF isto unity, the lower the error associated with the calibration. In thecase where the “assumed” thickness is equal to the “actual” thickness of20 Å as shown by curve 306, the CEF is equal to one at all wavelengthsand the calibration is perfectly accurate. In the situation where the“assumed” thickness is 25 Å (an error of just 5 Å) the CEF attains avalue of greater than 1.3 at short wavelengths, while maintaining avalue of less than 1.002 at wavelengths above 250 nm. This represents anerror of greater than 30% in the VUV and less than ˜0.2% at longerwavelengths. Hence, while silicon wafers may be readily used tocalibrate reflectometers at wavelengths greater than 250 nm, they do notprovide a practical means of accurately calibrating reflectometers inthe VUV.

An alternate approach to this problem is afforded by an embodiment ofthe current invention. The flowchart 502 depicted in FIG. 5 provides ageneral overview of the steps involved in the process. As is evidentfrom the figure the technique requires the use of two samples, astandard and a reference. The standard sample is chosen such that it isexpected to exhibit a significant and spectrally sharp CEF over somespectral region. The reference sample, on the other hand, is selectedsuch that it is expected to exhibit a relatively featureless reflectancespectrum over the same spectral region.

The first two steps 504 and 506 of the process are in effect identicalto those described in the conventional method of FIG. 1. Namely,knowledge of the properties of the standard sample is assumed, followingwhich the intensity of light reflected from the sample as a function ofwavelength is recorded and used to calibrate the reflectometer. At thispoint the calibrated reflectometer is used to measure a reference sampleand determine its reflectance as described in step 508. Once this hasbeen accomplished, in step 510 the “actual” properties of the standardsample are determined through evaluation of the measured reflectanceproperties of the reference sample and the CEF. With knowledge of the“actual” properties of the standard sample in hand, the reflectometercan then be accurately re-calibrated in step 512, thereby removingimprecision resulting from errors associated with the “assumed”properties of the standard sample in the second step of the process.Once the instrument has been re-calibrated the absolute reflectance ofunknown samples may be accurately determined as shown in step 514.

In one embodiment, the calibration techniques are dependent on thechoice of the standard sample. As discussed earlier, it is desirable forthe standard to exhibit a significant and spectrally sharp CEF spectrumover some spectral region of the reflectometer. To a great degree thiscapacity will be dictated by the optical nature of the sample.Specifically, the CEF signal generated by a standard sample is expectedto increase in the vicinity of an optical absorption edge correspondingto one or more of the materials comprising it. In this spectral regionsmall changes in the properties of the sample can generate significantchanges in the reflected signal and hence a large CEF contribution. Itfollows that it is thus desirable that the reflectometer has sufficientspectral resolution to ensure sharp features of the CEF signal aredetected and accounted for.

In a preferred embodiment of the invention, designed to calibrate a VUVreflectometer, the standard sample is comprised of a relatively thick(˜10000 Å) layer of SiO₂ deposited on a silicon substrate. FIG. 6presents a CEF plot for such a standard, wherein the ratios of threepairs of reflectance spectra are plotted for “assumed” SiO₂ thicknessesof 9990, 10000 and 10010 Å. As is evident from the graph, the spectra602 corresponding to the 9990 Å assumption and the spectra 604corresponding to the 10010 Å assumption both exhibit substantial andspectrally sharp CEF features (in the case where the “assumed” thicknessis equal to the “actual” thickness of 10000 Å the CEF is equal to one atall wavelengths). In fact, the data in the figure indicates that the 10Å error (representing just 1 part in 1000) would introduce an inaccuracyof greater than 200% in the VUV reflectance results.

In contrast to the CEF plot for the 20 Å SiO₂/Si sample presented inFIG. 4, wherein the CEF values at wavelengths longer than 250 nmdisplayed little in the way of error (owing to the fact that they allapproached unity even when the assumed and actual thicknesses were notthe same), the CEF values for the 10000 Å SiO₂/Si sample plotted in FIG.6 exhibit measurable error at virtually all wavelengths when the assumedand actual thickness are not the same. It is important to note, however,that the sharpest and most intense features in the CEF again occur inthe VUV (a direct consequence of the presence of the SiO₂ absorptionedge in this region).

While the 10000 Å SiO₂/Si sample provides an exemplary standard for thepurposes of the current invention, as a result of the significant CEFsignal it generates for small errors in “assumed” thickness, it will beclear to one skilled in the art that many other samples may functionequally as well. In general, any sample that produces a substantial CEFsignal for small error in “assumed” thickness or some other assumedsample property may be employed.

As defined within the scope of this disclosure, the CEF is essentially aratio of the “assumed” and “actual” reflectance spectra for a standard(or “calibration”) sample. If the assumptions regarding the standardsample are completely accurate, the CEF assumes a value of one at allwavelengths. If instead the assumptions are to some extent flawed, theCEF will display values greater or less than one. The greater theinaccuracies in the assumptions, the greater the CEF values will deviatefrom unity.

While the CEF clearly provides a sensitive indicator of calibrationaccuracy it is not, itself, observable. One aspect to exploiting the CEFis therefore to use the reference sample to render the CEF featuresapparent. This follows since all measurements performed on samplesfollowing the initial calibration are in effect the product of the CEFand the “actual” reflectance spectrum of the sample under study. Henceif the reference sample, with its substantially smooth and featurelessreflectance spectrum, is measured and if the CEF is not equal to unitythen the intense sharp features in the CEF will be clearly evident inthe reflectance spectrum recorded from the reference sample. Thus, evenwithout prior intimate knowledge of the “actual” reflectance propertiesof the reference sample (other than that the reference sample isrelatively featureless in the spectral region of interest) it ispossible to readily evaluate the characteristics of the CEF and hence,gauge the accuracy of the initial assumptions regarding the propertiesof the standard sample.

While any sample with a substantially smooth and featureless reflectancespectrum may be employed as a reference sample a particularlywell-suited choice may be a broad-band VUV mirror like the broad-bandVUV mirror having coating #1200 manufactured by Acton ResearchCorporation of the United States. A typical reflectance spectrum 702 forthis type of mirror is presented in FIG. 7. As is evident from thefigure this broad-band mirror combines high reflectance throughout theentire VUV region with a largely featureless spectrum. It may be notedfrom FIG. 7 that the reference sample does not display sharp features ina spectral region such as the VUV where the standard sample may displaya significant CEF. The sample used for a reference sample need notprovide a consistent reflectance spectrum from sample to sample. Forexample, the same type of broad-band VUV mirror with the same coatingfrom the same manufacturer may show a difference in absolute reflectancefrom mirror to mirror. However, if for any given mirror a relativelysmooth and featureless reflectance spectrum is provided (at least in thespectral range of interest), then the mirror may be suitable for use asa reference sample. Furthermore, even if the reference sample (such asthe mirror described above) exhibits absolute reflectance changes overtime, the sample may still be suitable as a reference sample. Thus, therepeatability of the manufacturing of the reference sample and thechanges in properties over time are not as significant as the sample'sfeatureless properties in the desired spectral range.

Thus, a technique is provided that includes utilizing a standard samplethat allows for calibration in the wavelengths of interest even when thestandard sample may exhibit significant reflectance variations at thosewavelengths for subtle variations in the properties of the standardsample. Calibration may be achieved even in cases where traditionallysignificant calibration error in regions of wavelengths that a user isinterested in would be expected to be encountered. In this regard thetechnique takes advantage of the presence of a certain amount ofcalibration error that may be referred to as a calibration errorfunction.

The calibration process may thus include a technique that utilizes afirst sample and a second sample. The first sample may includesignificant reflectance variation in the spectral region of interest asa function of sample property variations and the second sample may havea relatively featureless reflectance spectrum over the same spectralregion. The first sample may be considered a standard or calibrationsample and the second sample may be considered a reference sample. Byfirst calibrating the system using a standard sample and then measuringa reference sample, any sharp changes in the reflectivity observed fromthe reference sample may be assumed to be a function of the inaccuraciesin the assumptions regarding the calibration sample. With thisknowledge, the system may then be recalibrated.

Further, the calibration technique may utilize a standard sample thatmay have relatively unknown properties with the exception that it may beassumed to have a significant calibration error function in the spectralregions of interest. Thus, the exact properties of the standard sampleneed not be known if it can be assumed that the standard sample exhibitssharp changes in reflectance for changes in the sample property.

Before the reference sample measurement can be used to evaluate theresults of the calibration process it is desirable to mathematicallyconstruct a means of quantifiably assessing the CEF in light of itscoupling with the reference sample reflectance spectrum. In oneembodiment of the invention this may be generally accomplished in thefollowing manner.

First, the derivative of the measured reflectance spectrum iscalculated. This acts to reduce the coupling between the CEF and the“actual” reflectance spectrum of the reference sample and places greateremphasis on “sharp” reflectance structures (likely contributed by theCEF) than on slowly changing features (expected from the referencesample). Next, the absolute value of the derivative is calculated andthe resulting function integrated. Taking the absolute value of thederivative prior to integration is necessary in order to constructivelycapture both positive and negative values of the function and to avoidcanceling out contributions to the derivative arising from the referencesample reflectance spectrum. With the integration complete it ispossible to quantitatively evaluate the results of the initialcalibration procedure.

In this manner the integrated value can be fed back to an algorithm thatiteratively adjusts the initial assumptions regarding the properties ofthe standard sample, re-calculates the CEF and re-determines theintegrated value in an effort to minimize its value. When the minimumhas been achieved the “actual” properties of the standard sample, andhence its “actual” reflectance have been determined. At this point thereflectometer can be accurately calibrated and measurements on unknownsamples performed.

A further understanding of the steps involved in this method may berealized following a review of the data presented in FIGS. 8-11. FIG. 8presents the results of a measurement performed on an appropriatereference sample following calibration with a 10000 Å SiO₂/Si standardsample using an “assumed” thickness of 10010 Å. The sharp structureevident in the measured spectrum of the reference sample (adjusted forthe calibration) is a consequence of the 10 Å error introduced duringthe calibration process. Signal 802 shown in FIG. 8 is a measuredspectrum obtained from the reference sample. This signal is a result ofthe product of the reflectance of the reference sample and the CEFspectrum resulting from the inaccurate calibration. At this point in theprocess, the CEF and reference sample reflectance signals areessentially coupled, and as is evident exist largely at shorterwavelengths in the VUV. In the present example, this occurs because theCEF signal was largely present in the VUV region and the referencereflectance was substantially featureless in this same region.

The derivative of this spectrum is presented in FIG. 9. Notsurprisingly, the bulk of the CEF/reference reflectance productderivative signal 902 still resides in the VUV region of the spectrum.The absolute value of the trace is then calculated prior to integration,which ultimately yields a quantitative measure of calibration accuracy.This integrated sum is then returned to an iterative routine thatadjusts the “assumed” thickness of the standard sample and re-calculatesthe CEF/reference reflectance product integral until its value isminimized.

Values of the CEF/reference reflectance product integral as a functionof “assumed” thickness are presented in the sensitivity plot of FIG. 10for the 10000 Å SiO₂/Si standard sample with and without noise added tothe system. Plot 1002 illustrates the values of the CEF/referencereflectance product integral including the presence of a 0.5% noisecomponent while plot 1004 shows the data without noise. As is evidentfrom examination of the data, the integral is extremely sensitive tosmall errors in the “assumed” thickness of the SiO₂ layer, even in thepresence of a 0.5% noise component in the raw reflectance data. Needlessto say, the minimum value of the CEF/reference reflectance productintegral is achieved when the “assumed” thickness value matches the“actual” thickness of the standard sample. Following completion of theiterative process the “actual” properties of the standard sample aredetermined and the instrument is accurately calibrated. At this point intime the CEF function assumes a value of unity at all wavelengths andsubsequent measurement of the reference sample yields its truereflectance spectrum 1102, as illustrated in FIG. 11.

An exemplary and detailed description of this calibration procedure isoutlined in the flowchart 1202 of FIG. 12 wherein the mathematicalrelationships involved in calculating the absolute reflectance of anunknown sample are presented. As shown in FIG. 12 step 1204, first theassumed knowledge of a standard sample, expected to exhibit substantialcalibration error features in a given spectral region is used tocalculate the assumed reflectance of the standard sample. In step 1206the intensity from the standard sample is recorded. In step 1208, thesource intensity profile is calculated using the assumed reflectance ofthe standard sample. The intensity from the reference sample that isexpected to exhibit substantially smooth reflectance properties over thesame spectral region is then recorded in step 1210. Next, in step 1212the reflectance of the reference sample is calculated. The reflectanceof the reference sample may be then expressed according to the equationof step 1214. The absolute value of the derivative of the referencesample reflectance spectrum may then be calculated in step 1216. Theintegral of the absolute value of the derivative is then calculated instep 1218. Next, in step 1220 an iterative adjustment of the assumptionsregarding the properties of the standard sample is performed and theassumed reflectance of the standard is re-calculated. Control isreturned to step 1214 from step 1220 until the value of the integral isminimized and the actual properties of the standard sample are thusobtained at which point the process proceeds from step 1220 to step1222. In step 1222 the source intensity profile is re-calculated usingthe actual reflectance of the standard. The intensity of an unknownsample is then recorded in step 1224. Finally, the reflectance of theunknown sample is calculated and expressed according to the equation ofstep 1226.

It will be recognized by those skilled in the art that many othermethods exist for quantifying the CEF signal in such a manner as torender it useful for feedback to an iterative routine designed tominimize its value through adjustments in the “assumed” properties ofthe standard sample. In addition, while the above discussions haveregarded the thickness of the standard sample as being the “assumed”property to be accurately determined during the calibration process, itwill be further apparent to those skilled in the art that many otherproperties of the standard sample could also be treated as “assumed”properties and determined in the same manner. Such properties couldinclude, but are not limited to, complex refractive index, composition,porosity and surface or interface roughness. These properties may bedetermined independently, or in some instances simultaneously along withother properties during the calibration procedure.

In certain circumstances additional mathematical steps may be performedto enhance the performance of the calibration routine. In the presenceof significant noise in the measured reflectance data recorded from thereference sample it may be advantageous to filter the raw data prior toor after taking its derivative. While many appropriate smoothing filtersexist in the prior art, the Savitzky-Golay filter is particularlywell-suited to this application as it generally preserves the width andposition of spectral features in the raw data. Additionally, in somesituations it may prove beneficial to limit the range of wavelengthsover which the integration is performed in order to further emphasizethe contribution of the CEF signal.

It will be clear to those skilled in the art that the present inventionreadily lends itself to many modes of implementation. A particularlyadvantageous approach would be to integrate the reference sample intothe reflectometer such that it could be effortlessly utilized. Thisapproach is described in detail in U.S. application Ser. No. 10/668,644,filed on Sep. 23, 2003, which discloses a vacuum ultraviolet referencingreflectometer and in U.S. application Ser. No. 10/909,126 filed Jul. 30,2004, the disclosures of which are incorporated herein by reference. Anexample of the use of the calibration techniques provided herein incombination with the systems described in the aforementioned prior filedU.S. Applications is illustrated in FIG. 12A. FIG. 12A provides abroadband reflectometer system 3400 as described in more detail withregard to FIG. 34 in U.S. application Ser. No. 10/909,126 filed Jul. 30,2004. The system 3400 may optionally include multiple sources 3201,3206, and 3302 and corresponding multiple spectrometers 3214, 3216, and3304. Flip-in mirrors FM-1 through FM-4 and corresponding windows W-3through W-6 may be utilized to select the various sources andspectrometers. Mirrors M-1 through M-5 are utilized to direct the beamsas shown. A sample 3206 may be located in a sample beam 3210. Areference beam 3212 is also provided. A beam splitter BS is provided andshutters S-1 and S-2 select which of the beams is being utilized. Thevarious optics and samples may be included in environmentally sealedchambers 3202 and 3204 such that measurements in the VUV bandwidth maybe obtained.

As shown in FIG. 12A, a sample beam (or channel) 3210 is provided forobtaining measurements from a sample 3206. A reference beam (or channel)3212 is provided for referencing the system. Generally, the referencebeam is configured to provide a mechanism that is indicative ofenvironmental or other system conditions. The reference beam may beconfigured to provide a beam path that is similar in beam length andenvironmental conditions as the sample beam, however, the reference beamdoes not encounter the sample 3206. In operation with the calibrationtechniques described herein, the standard sample may be placed at thesample 3206 location of FIG. 12A. A separate reference sample need notbe placed at the sample 3206 location however (although such a use of aseparate reference sample placed at the sample 3206 location may beutilized). Rather, the entire reference beam 3212 path may be construedas the “reference sample.” For example, the cumulative effects of thebeam splitter BS, mirror M-4, window W-2, and mirror M-5 (i.e. theelements that are different between the sample and reference paths) maybe construed as together forming the “reference sample.” Such use of anentire beam path for the reference sample is generally available if thecombined effect of the optical elements provides a relatively smoothfeatureless reflectance spectrum in the spectral range of interest. Itwill be recognized that many other methods of utilizing the calibrationtechniques will be apparent to one skilled in the art and thecalibration techniques described herein are not limited to themechanical configurations referred to herein. Though not shown, thereflectometer system 3400 may include a processor, computer, otherelectronics, and/or software for calibrating the system according to thecalibration techniques provided herein. The processor, computer, otherelectronics, and/or software may be constructed integral with thereflectometer optical hardware or may be a separate stand alone unitthat together with the reflectometer optical hardware forms areflectometer system configured to allow for calibration.

There are many advantages afforded by the current invention. One suchadvantage is that it provides a technique by which VUV reflectometrydata may be accurately calibrated in light of the fact thatuncertainties associated with commercially available thin film standardsamples may be too large to enable accurate calibration usingconventional methods. As a result, it may altogether eliminate the needfor reflectometer tool users to purchase, maintain and re-calibrateexpensive standard samples.

Furthermore, the current invention allows one to achieve highly accuratecalibration results without prior knowledge of the exact properties ofeither the standard or reference samples. This capability isparticularly useful since virtually all samples can be expected toundergo subtle changes in their properties as a function of time, as aresult of either natural growth mechanisms or contamination.

While particularly well-suited to the purpose of calibrating VUVreflectometry data, the present invention may also be used to calibratereflectometry data from other spectral regions. In such instances it maybe advantageous to employ the use of other standard samples which couldbe expected to generate substantial CEF signals in the spectral regionof interest.

A further advantage of the invention is that it does not require use ofa secondary reference instrument, thereby greatly reducing system costand complexity.

Once reflectance data has been recorded from a calibrated reflectometerit is typically sent to a processor unit where it is subsequentlyreduced via analytical algorithms. These algorithms generally relateoptical data, such as reflectance, to other properties of the sample,which can then be measured and/or monitored like film thickness, complexrefractive index, composition, porosity, surface or interface roughness,etc.

Data reduction is generally accomplished using some form of the FresnelEquations in combination with one or more models to describe the opticalproperties of the materials comprising the sample. Regardless of thespecific model used in the reduction of the data set, the greater goalis generally to use a mathematical expression to describe the measureddata such that certain parameters, relating to the properties of thesamples (as discussed above), can be obtained through an iterativeoptimization process. That is, the measured data set is compared to onecalculated using an expression that depends on a set of parametersrelating to the nature of the sample. The discrepancy between themeasured and calculated data sets is minimized by iteratively adjustingthe values of the parameters until such time as adequate agreementbetween the two data sets is achieved. This discrepancy is usuallyquantified in terms of a “goodness of fit” (GOF) parameter.

Numerous mathematical expressions for calculating GOF exist in the priorart. Most of these techniques are to some degree based on adetermination of the difference between the measured and calculatedspectra. While these methods are generally applicable and do areasonable job of locating the general region of the absolute minimum inparameter space, they often exhibit shortcomings upon convergence atthat minimum, particularly in the presence of increasing levels of noisein the measured data.

FIG. 13 presents a sensitivity plot 1302 for a prior art GOF expression(known to those skilled in the art as the “Chi-square” merit function)as calculated for a 10000 Å SiO₂/Si test sample. As is evident thisstandard merit function provides an effective means of locating thegeneral region of the “actual” thickness of the film, as it exhibits arelatively smooth line shape with a well-defined minimum. On closerexamination, however, the sensitivity of the function is seen to degradesignificantly in the immediate vicinity of the minimum. This point isbetter illustrated in FIG. 14, which presents an expanded view 1402 ofthe sensitivity plot 1302 of FIG. 13 in the presence of 1% noise in themeasured reflectance data.

As is evident upon examination of the data in FIG. 14 the 1% noiseresident in the raw reflectance data significantly reduces the abilityof the merit function to enable the minimization routine to convergeupon the “actual” thickness of the test sample. Hence, it would bedesirable to develop a superior method of determining the “actual”thickness once the routine has located the general vicinity of thesolution.

Another preferred embodiment of the present invention provides thiscapability. Namely, it provides a highly sensitive measure ofconvergence that can be used in combination with an appropriateminimization routine to efficiently reduce measured reflectance data,thus yielding results exhibiting a higher level of accuracy thenattainable using conventional techniques alone. While designed to beused in conjunction with traditional merit functions, the currentinvention may in some instances altogether supplant the use of suchmethods.

A general overview of one embodiment of the data reduction techniquesdescribed herein is presented in the flowchart 1502 of FIG. 15, whereinthe mathematical relationships involved in an iterative data fittingroutine associated with the measurement of an unknown sample using areflectometer are presented. The first step 1504 in the process is toobtain the absolute reflectance spectrum of the unknown sample using anaccurately calibrated reflectometer. Once this spectrum has beenrecorded the initial assumptions regarding the physical properties ofthe sample are used to calculate the “expected” reflectance propertiesof the sample in step 1506. With these two spectra in hand the ratio ofthe “expected” to “measured” spectra is determined as shown in theequation of step 1508.

This ratio, termed herein as the measurement error function (MEF), issimilar in nature to the CEF discussed earlier. While both functionsrelate the ratio of “assumed” to “actual” data sets, the MEF is somewhatsimpler to evaluate as it is not coupled with the reflectance of thereference sample. That is, during minimization the CEF is evaluatedthrough examination of the reference sample reflectance spectrum, whilethe MEF is evaluated through examination of the reflectance of theunknown sample itself.

Before the MEF (or reflectance spectrum ratio) can be used to evaluatethe results of the minimization routine a suitable merit function mustagain be constructed. Following the approach undertaken with the CEFearlier, the next step in the flowchart 1502 is to calculate theabsolute value of the derivative of the MEF as shown in step 1510. Thisacts to accentuate sharp spectral features in the MEF, resulting largelyfrom wavelengths in the vicinity of the absorption edge for one or morematerials comprising the unknown sample. At this point the absolutevalue of the derivative is calculated and then the resulting function isintegrated as shown in step 1512. As before, taking the absolute valueof the derivative prior to integration is desirable in order toconstructively capture both positive and negative values. Once theintegration is complete it is possible to quantitatively evaluate theresults of the reduction process. More particularly, an iterativeprocess of adjusting assumptions regarding properties of the unknownsample and recalculating the expected reflectance spectrum of theunknown sample may occur as shown in step 1514. After the recalculationof the expected reflectance spectrum, control passes again to step 1508and steps 1508-1514 are repeated until a value of the integral isminimized at which point the actual properties of the unknown sample aredetermined to have been obtained and control is passed to step 1516where the actual properties of the unknown sample are provided as anoutput.

It is noted that this technique is insensitive to fixed offsets betweenthe “assumed” and “measured” reflectance spectra. That is, it can not beeffectively used to reduce long wavelength reflectometry data collectedfrom samples comprised of very thin films (i.e. thin enough so as not togive rise to significant interference effects) since such data sets areunlikely to contain sharp spectral features that are required by thismethod. Fortunately, in the VUV region virtually all thin film samplesexhibit some form of sharp structure in their reflectance spectra,resulting from either interference or absorption effects.

To better demonstrate the superior performance of this approach,relative to that of the conventional Chi-square method, FIG. 16 presentsan expanded sensitivity plot 1602 calculated using an embodiment of thecurrent invention for the same 10000 Å SiO₂/Si test sample of FIG. 14.Comparing the results in these two figures it is shown that the presentinvention is less affected by the 1% noise level present in the rawreflectance data, than is the Chi-square method. This establishes thatthe current invention provides the optimization routine with a moreeffective measure of the fit minimum and hence, the “actual” thicknessof the film. This improved performance demonstrates that at least whenthe “assumed” thickness value is in the general vicinity of the “actual”thickness the current invention is capable of achieving a more accurateand repeatable result than is possible using conventional methods.

Exploration of a larger parameter space demonstrates why, in somesituations, the current invention is best utilized in conjunction withprior art methods. The reasons for this become evident upon examinationof FIG. 17 which presents a sensitivity plot 1702 calculated using thecurrent invention for the 10000 Å SiO₂/Si sample graphed over a widerrange of “assumed” thickness values. While the value of the MEF integralat the “actual” thickness is clearly distinguishable from its value atall other “assumed” thicknesses, the sharp features in the line shape ofthe MEF integral render it computationally arduous to fit. Hence, itwould more efficient to begin searching for the minimum using aChi-square based merit function and then once apparent convergence hadbeen achieved, switch over and continue searching for the “actual”minimum using the current invention. In this sense the use of thecurrent invention represents a high resolution mode of reflectometeroperation.

In other situations, it may be possible to recognize the benefitsafforded by the current invention without also employing the use ofconventional Chi-square methods. An example of one such situation is themeasurement of a 100 Å SiO₂/Si sample in the presence of 1% noise in themeasured reflectance data. In this circumstance the global searchperformance of the present invention is comparable to that of thestandard Chi-square method. Evidence of this is provided by thesensitivity plot comparison presented in FIG. 18. As shown in FIG. 18, asensitivity plot 1802 of the standard Chi-square method is compared to asensitivity plot 1804 utilizing the MEF techniques according to thepresent invention. While both functions exhibit relatively smooth lineshapes it is noted that the influence of the 1% noise in the reflectancedata is already evident in the Chi-square results.

FIGS. 19 and 20 present expanded sensitivity plots covering a 4 Å regionin the vicinity of the “actual” thickness of the 100 Å SiO₂/Si samplecalculated using the MEF technique of the present invention (sensitivityplot 1902 of FIG. 19) and the Chi-square method (sensitivity plot 2002of FIG. 20) respectively. Comparisons of these two figures demonstratethe advantageous performance of the present invention in this situation.

Thus, data measurements may be obtained by utilizing a fitting routinethat includes at least a portion of the routine that is a spectrallydriven fitting routine rather than relying solely on an amplitude drivenroutine (which typically incorporates difference calculations). Moreparticularly, measurements may be obtained by utilizing the presence ofsharp, narrow spectral features. In one embodiment utilizing a spectraldriven routine, a ratio of an expected reflectance spectrum of thesample being measured to the actual reflectance spectrum of the samplebeing measured. Rather than being based upon a difference between theexpected and actual values, the techniques provided herein utilize aratio of the values. The derivative of this ratio may be utilized toaccentuate sharp spectral features.

These spectrally driven techniques are particularly useful in spectralregions that contain sharp spectral features, for example such as thesharp features that thin films often exhibited in the VUV region. Thus,a data convergent technique is provided that may beneficially utilize anabsorption edge effect of the material is disclosed. In this mannersharp spectral features, for example resulting from either interferenceor absorption effects are advantageously utilized to better determine adata minimum that is indicative of an actual measurement value. Themerit function presented in the present disclosure may therefore bedriven by the absorption properties of the material being measured withan emphasis on regions that encompass large changes in absorption (theabsorption edges) for small changes in sample properties.

The data reduction techniques may utilize a two step approach. In suchan embodiment a low resolution step such as an amplitude driven fittingroutine may be used to first provide a “coarse” measurement. Then a highresolution step such as a spectrally-driven fitting routine thatadvantageously utilizes the presence of sharp spectral features may beused to then provide a “fine” measurement. In one approach for such atechnique, a low resolution approach may be utilized to obtain a roughmeasurement value by using a difference based technique such as in a“Chi-square” merit function and then a more accurate determination ofthe actual measurement value may be obtained by utilizing the spectrallydriven ratio based technique in the region of interest initiallyidentified by the low resolution technique.

The techniques provided herein may be construed as dynamically weightingthe results for regions in which the sharp spectral features arepresent. For example with regard to sharp spectral edges present in theVUV range, these techniques may be construed as applying a weightingfunction which strongly emphasizes the VUV and strongly de-emphasizesthe DUV and longer wavelength data where sharp spectral features may notbe expected for a given sample. Further, the process may be weightedsuch that only measured data that could reasonably be expected tocontain useful information may be included. This weighting method may bedynamic since the decision making process (which measured data should beconsidered) could be repeated after each iteration.

While the examples presented herein have addressed utilization of thetechnique to facilitate accurate measurements of film thickness, it willbe apparent to those skilled in the art that other preferred embodimentsof the invention can be employed equally well in the measurement ofother material properties including, but not limited to complexrefractive index, composition, porosity, surface or interface roughness,etc. Additionally, while the examples presented herein have dealtspecifically with the measurement of SiO₂/Si samples, it will be clearthat many other types of samples may be measured equally well using thedescribed methods. For example, the techniques provided herein may beutilized when analyzing more complex stacks of thin films.

Examples of such stacks include thin film SiO₂/SiN stacks on a substrateor thin film SiN/SiO₂/SiN stacks on a substrate.

As discussed earlier, the heightened levels of sensitivity afforded bythe current invention results largely from the fact that it exploits thesubstantial changes in reflectance signal that accompany small changesin the properties of samples when in the vicinity of the opticalabsorption edge of one or more of the materials comprising such samples.While such features commonly lie in the VUV spectral region, thetechnique can also be generally applied at longer wavelengths insituations where substantially sharp features are expected in the MEF asa result of subtle changes in the physical properties of the samplesunder study.

It will be recognized by those skilled in the art that many othermethods for quantifying the MEF signal in such a manner as to render ituseful for feedback to an iterative routine designed to minimize itsvalue through adjustments in the “assumed” properties of the measuredsample exist. Furthermore, it will also be readily apparent that in somecircumstances additional mathematical steps may be performed to enhancethe performance of the measurement routine.

Further modifications and alternative embodiments of this invention willbe apparent to those skilled in the art in view of this description.Accordingly, this description is to be construed as illustrative onlyand is for the purpose of teaching those skilled in the art the mannerof carrying out the invention. It is to be understood that the forms ofthe invention herein shown and described are to be taken as presentlypreferred embodiments. Equivalent elements may be substituted for thoseillustrated and described herein and certain features of the inventionmay be utilized independently of the use of other features, all as wouldbe apparent to one skilled in the art after having the benefit of thisdescription of the invention.

1. A reflectometer system, comprising: a light source that is utilizedto create a sample channel light path; a location in the reflectometersample channel light path for placement of a standard sample; a locationin the reflectometer for the placement of a reference sample; and aspectrometer configured to collect reflectance data from the standardsample and the reference sample; wherein the reflectometer is calibratedby utilizing the presence of significant reflectance variations from thestandard sample that result from variations of actual properties of thestandard sample from the assumed properties of the standard sample. 2.The reflectometer system of claim 1, wherein the reference sample andthe standard sample locations are the same.
 3. The reflectometer systemof claim 1, wherein the reference sample and standard sample locationsare different.
 4. The reflectometer system of claim 1, wherein thereference sample is at least one broadband mirror.
 5. The reflectometersystem of claim 1, wherein the reference sample is comprised of aplurality of optical elements.
 6. The reflectometer system of claim 5,wherein the reference sample is comprised of a plurality of broadbandmirrors.
 7. The reflectometer of claim 1, wherein the reference sampleis formed by the use of a reference channel light path that is separateat least in part from a sample channel light path.
 8. A reflectionmeasurement apparatus which operates below deep ultra-violet (DUV)wavelengths, the apparatus comprising: at least one light source, the atleast one light source providing a source beam including wavelengthsbelow DUV wavelengths; a sample channel light path; a reference channellight path, wherein the reference channel light path is configured tocomprise a reference sample that is relatively spectrally featureless inat least some of the vacuum ultra-violet (VUV) wavelength region; aspectrometer that receives light from the sample channel light path andthe reference channel light path; and at least one optical elementselectively enabling or disabling at least one of the reference channellight path or the sample channel light path; wherein the reflectionmeasurement apparatus is configured to be calibrated by utilizing in thesample channel light path a standard sample that has a significantcalibration error function in at least a portion of the VUV wavelengthregion.
 9. The reflection measurement apparatus of claim 8, wherein thereference sample comprises at least one mirror.
 10. The reflectionmeasurement apparatus of claim 9, wherein the reference sample comprisesat least one broadband VUV mirror.
 11. The reflection measurementapparatus of claim 9, wherein the reference sample comprises a pluralityof optical elements.
 12. The reflection measurement apparatus of claim11, wherein the reference sample comprises a plurality of mirrors.